Sampling Distribution of the Difference Between Independent Pearson r's (2 of 2)


Start by computing the mean and standard deviation of the sampling distribution of the difference between z's. As can be calculated with the help of the r to z' procedure, r's of .6 and .5 correspond to Z's of .69 and .55 respectively. Therefore the mean of the sampling distribution is:

0.69-0.55 = 0.14.

The standard deviation is:

The portion of the distribution for which the difference is negative (the correlation in the female sample is lower) is shaded. What proportion of the area is this?

A difference of 0 is: standard deviations above (0.58 sd's below) the mean. A z table can be used to calculate that the probability of a z less than or equal to -0.58 is 0.28. Therefore the probability the the correlation will be lower in the female sample is 0.28.